[latex]f\\left(x\\right)=d\\left(x\\right)q\\left(x\\right)+r\\left(x\\right)[\/latex] where [latex]q\\left(x\\right)\\ne 0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Key Concepts<\/h2>\n
\n \t
Polynomial long division can be used to divide a polynomial by any polynomial with equal or lower degree.<\/li>\n \t
The Division Algorithm tells us that a polynomial dividend can be written as the product of the divisor and the quotient added to the remainder.<\/li>\n \t
Synthetic division is a shortcut that can be used to divide a polynomial by a binomial of the form x \u2013 k<\/em>.<\/li>\n \t
Polynomial division can be used to solve application problems, including area and volume.<\/li>\n<\/ul>\n
Glossary<\/h2>\n
\n \t
Division Algorithm<\/strong><\/dt>\n \t
given a polynomial dividend [latex]f\\left(x\\right)[\/latex] and a non-zero polynomial divisor [latex]d\\left(x\\right)[\/latex] where the degree of [latex]d\\left(x\\right)[\/latex] is less than or equal to the degree of [latex]f\\left(x\\right)[\/latex], there exist unique polynomials [latex]q\\left(x\\right)[\/latex] and [latex]r\\left(x\\right)[\/latex] such that [latex]f\\left(x\\right)=d\\left(x\\right)q\\left(x\\right)+r\\left(x\\right)[\/latex] where [latex]q\\left(x\\right)[\/latex] is the quotient and [latex]r\\left(x\\right)[\/latex] is the remainder. The remainder is either equal to zero or has degree strictly less than [latex]d\\left(x\\right)[\/latex].<\/dd>\n<\/dl>\n
\n \t
synthetic division<\/strong><\/dt>\n \t
a shortcut method that can be used to divide a polynomial by a binomial of the form x<\/em> \u2013 k<\/em><\/dd>\n<\/dl>\n\n","rendered":"
Key Equations<\/h2>\n
\n\n
\n
Division Algorithm<\/td>\n
[latex]f\\left(x\\right)=d\\left(x\\right)q\\left(x\\right)+r\\left(x\\right)[\/latex] where [latex]q\\left(x\\right)\\ne 0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Key Concepts<\/h2>\n
\n
Polynomial long division can be used to divide a polynomial by any polynomial with equal or lower degree.<\/li>\n
The Division Algorithm tells us that a polynomial dividend can be written as the product of the divisor and the quotient added to the remainder.<\/li>\n
Synthetic division is a shortcut that can be used to divide a polynomial by a binomial of the form x \u2013 k<\/em>.<\/li>\n
Polynomial division can be used to solve application problems, including area and volume.<\/li>\n<\/ul>\n
Glossary<\/h2>\n
\n
Division Algorithm<\/strong><\/dt>\n
given a polynomial dividend [latex]f\\left(x\\right)[\/latex] and a non-zero polynomial divisor [latex]d\\left(x\\right)[\/latex] where the degree of [latex]d\\left(x\\right)[\/latex] is less than or equal to the degree of [latex]f\\left(x\\right)[\/latex], there exist unique polynomials [latex]q\\left(x\\right)[\/latex] and [latex]r\\left(x\\right)[\/latex] such that [latex]f\\left(x\\right)=d\\left(x\\right)q\\left(x\\right)+r\\left(x\\right)[\/latex] where [latex]q\\left(x\\right)[\/latex] is the quotient and [latex]r\\left(x\\right)[\/latex] is the remainder. The remainder is either equal to zero or has degree strictly less than [latex]d\\left(x\\right)[\/latex].<\/dd>\n<\/dl>\n
\n
synthetic division<\/strong><\/dt>\n
a shortcut method that can be used to divide a polynomial by a binomial of the form x<\/em> \u2013 k<\/em><\/dd>\n<\/dl>\n\n\t\t\t \n\t\t\t